Related papers: Newman's theorem via Carath\'eodory
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver…
It is known that the classical Frobenius theorem on conditions of integrability for distributions of planes can be extended to the case of complex holomorphic distributions. We show that an alternative criterion for integrability, namely,…
A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
We prove that the fidelity of two exemplary communication complexity protocols, allowing for an N-1 bit communication, can be exponentially improved by N-1 (unentangled) qubit communication. Taking into account, for a fair comparison, all…
This work studies distributed learning in the spirit of Yao's model of communication complexity: consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform some…
In this paper, we use the Carath\'eodory Convergence Theory to prove a landing theorem of rays in hyperbolic components with rational arguments. Although the proof is done in the setting of a family of entire transcendental maps with two…
We survey the classical results of the Dirichlet Approximation Theorem.
In the Telephone Broadcasting problem, the goal is to disseminate a message from a given source vertex of an input graph to all other vertices in the minimum number of rounds, where at each round, an informed vertex can send the message to…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical…
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
It is well--known that certain properties of continuous functions on the circle $\mathbb T$, related to the Fourier expansion, can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
The paper contains a simple proof of the classical Hahn decomposition theorem for charges and, as a corollary, an explicit measurable in parameter construction of a Radon-Nikodym derivative of one measure by another.
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…
This paper surveys the theory of compactness of the d-bar-Neumann problem. It also contains several results which improve upon what was previously known.